Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int a[111][111], r[111], c[111];
int main() {
  int n, m, i, j, f, s;
  cin >> n >> m;
  f = 0;
  if (n > m) f = 1;
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= m; j = j + 1) {
      if (f)
        cin >> a[j][i];
      else
        cin >> a[i][j];
    }
  if (f) swap(n, m);
  s = 0;
  for (i = 1; i <= n; i = i + 1) {
    r[i] = 1 << 30;
    for (j = 1; j <= m; j = j + 1) r[i] = min(r[i], a[i][j]);
    s += r[i];
    for (j = 1; j <= m; j = j + 1) a[i][j] -= r[i];
  }
  for (j = 1; j <= m; j = j + 1) {
    c[j] = 1 << 30;
    for (i = 1; i <= n; i = i + 1) c[j] = min(c[j], a[i][j]);
    s += c[j];
    for (i = 1; i <= n; i = i + 1) a[i][j] -= c[j];
  }
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= m; j = j + 1)
      if (a[i][j] != 0) {
        cout << "-1\n";
        return 0;
      }
  if (f) {
    swap(n, m);
    for (i = 1; i <= max(n, m); i = i + 1) swap(r[i], c[i]);
  }
  cout << s << endl;
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= r[i]; j = j + 1) cout << "row " << i << endl;
  for (j = 1; j <= m; j = j + 1)
    for (i = 1; i <= c[j]; i = i + 1) cout << "col " << j << endl;
  return 0;
}